Local simulation of singlet statistics for a restricted set of measurements

The essence of Bell’s theorem is that, in general, quantum statistics cannot be reproduced by a local hidden variable (LHV) model. This impossibility is strongly manifested when statistics collected by measuring certain local observables on a singlet state, violates the Bell inequality. In this work, we search for local POVMs with binary outcomes for which an LHV model can be constructed for a singlet state. We provide various subsets of observables for which an LHV model can be provided for singlet statistics.

[1]  M. Genovese.  Research on hidden variable theories: A review of recent progresses , 2005, quant-ph/0701071.

[2]  Nicolas Gisin,et al.  Simulation of partial entanglement with nonsignaling resources , 2008, 0803.2359.

[3]  Md. Rajjak Gazi,et al.  A complementary relation between classical bits and randomness in local part in the simulating singlet state , 2010, 1009.6161.

[4]  M. Hall,et al.  Complementary contributions of indeterminism and signaling to quantum correlations , 2010, 1006.3680.

[5]  Sophie Laplante,et al.  Classical simulation of traceless binary observables on any bipartite quantum state , 2007 .

[6]  Manik Banik,et al.  Optimal free will on one side in reproducing the singlet correlation , 2012, 1204.3835.

[7]  R. Cleve,et al.  Nonlocality and communication complexity , 2009, 0907.3584.

[8]  J. Barrett.  Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality , 2001, quant-ph/0107045.

[9]  J. Bell.  On the Einstein-Podolsky-Rosen paradox , 1964 .

[10]  N. Gisin.  Bell's inequality holds for all non-product states , 1991 .

[11]  Paul Busch,et al.  Some realizable joint measurements of complementary observables , 1987 .

[12]  C. Ross.  Found , 1869, The Dental register.

[13]  Sophie Laplante,et al.  Simulating quantum correlations as a distributed sampling problem (9 pages) , 2005, quant-ph/0507120.

[14]  N. Gisin,et al.  Maximal violation of Bell's inequality for arbitrarily large spin , 1992 .

[15]  Antonio Acin,et al.  Genuine tripartite entangled states with a local hidden-variable model , 2006 .

[16]  N. Gisin,et al.  How much measurement independence is needed to demonstrate nonlocality? , 2010, Physical review letters.

[17]  Popescu,et al.  Bell's inequalities versus teleportation: What is nonlocality? , 1994, Physical review letters.

[18]  N J Cerf,et al.  Simulating maximal quantum entanglement without communication. , 2005, Physical review letters.

[19]  M. Hall.  Local deterministic model of singlet state correlations based on relaxing measurement independence. , 2010, Physical review letters.

[20]  D. Bacon,et al.  Communication cost of simulating Bell correlations. , 2003, Physical review letters.

[21]  G. Röpke,et al.  Operational Quantum Physics , 1997 .

[22]  B. S. Cirel'son.  Quantum generalizations of Bell's inequality , 1980 .

[23]  M. Hall,et al.  Relaxed Bell inequalities and Kochen-Specker theorems , 2011, 1102.4467.

[24]  G. Kar,et al.  Unsharp observables and objectification problem in quantum theory , 1999 .

[25]  P. Busch,et al.  Unsharp reality and joint measurements for spin observables. , 1986, Physical review. D, Particles and fields.

[26]  A. Shimony,et al.  Proposed Experiment to Test Local Hidden Variable Theories. , 1969 .

[27]  S. Popescu,et al.  Generic quantum nonlocality , 1992 .

[28]  K. Kraus,et al.  States, effects, and operations : fundamental notions of quantum theory : lectures in mathematical physics at the University of Texas at Austin , 1983 .

[29]  Werner,et al.  Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. , 1989, Physical review. A, General physics.